The use of elastomers for high strain rate applications, such as skid resistant tire treads, mechanical capacitors, and coatings for impact resistance and acoustic damping, requires the ability to measure the stress-strain behavior to failure at high strain rates, for example, greater than 10 s−1. Often the function of such materials in high strain rate applications is to absorb energy. The amount of absorbed energy is related to the area under the stress-strain curve. The stress-strain behavior of polymers depends strongly on the strain rate; that is, elastomers are highly viscoelastic. The strain rate in many applications is higher than that measured with conventional experimental tests. Characterizing elastomers at high strain rates is difficult, even at small amplitudes.
Typical dynamic mechanical spectrometers are limited to frequencies below about 100 Hz, although custom-built instruments have attained 10 kHz. Atomic force microscopes (“nanoindenters”) operate as high as 1 MHz but only probe the surface. While time-temperature superpositioning is often invoked to extend the effective frequency range of test data, the results are inaccurate for measurements in the glass transition zone. Unfortunately, this is often the regime of interest if very high frequency results are required. The difficulties of high strain rate testing are exacerbated if the behavior at high strains is to be measured. Even though unfilled rubber can be linearly viscoelastic to fairly large strains (about 100%), it is generally not possible to apply Boltzmann superpositioning to deduce the properties at high strains from low strain experiments.
There are available high speed tensile test machines. However, most do not provide the full stress-strain to failure curves to high elongation. While present-day devices, such as the tensile split Hopkinson pressure bar and the expansion ring tests, can provide dynamic stress-strain curves at very high rates, they are not designed to monitor how the specimen fractures. Moreover, there is a mixed mode of deformation, which does not correspond to homogeneous strain such as uniaxial deformation. There is a need for a tensile impact test machine that gives both dynamic stiffness and strength characteristics of rubber and soft polymeric materials and is capable of monitoring specimen fracture.
The stress-strain response of polymeric materials to high strains (up to about 10) at high strain rates (up to about 104 s−1) is an unexplored area of behavior. The performance in such applications often depends on the details of the stress-strain response, which for polymers depends strongly on strain rate. A number of devices have been developed for measuring the mechanical response of polymers at high speed, but many do not allow visual observation of specimen deformation and failure. Other devices, such as the split Hopkinson pressure bar, are limited in the range of strain that can be applied. See B. Hopkinson, Philos. Trans. R. Soc. London, Ser. A 213, 437 (1914) and H. Kolsky, Proc. Phys. Soc. London, Sect. B 62, 676 (1949).
Previously, various methods have been explored for measurement of the mechanical response of elastomers at high strain rates. Albertoni, et al, Rubber Chem. Technol. 10, 317 (1937) modified a pendulum hammer to stretch a ring-shaped test piece to a predetermined elongation at constant strain rates up to about 40 s−1. A pin is placed at a predetermined distance, which disengages the test specimen from the pendulum. Following the release of the rubber sample, the pendulum continues to a new height, as determined by the retained energy. The difference in the initial and follow-through heights of the pendulum yields the energy to deform the sample. A different test specimen is used for each point, so that by repeated tests at various strains (i.e., pin positions) the stress/extension curve is obtained. Note however that the stress at any given strain corresponds to the average of all lower strains; this means that the secant modulus value is measured, not the actual tangent modulus.
Roth and Holt, Rubber Chem. Technol. 13, 348 (1940), designed an instrument that used a falling weight, achieving strain rates up to 20 s−1. A ring-shaped specimen is stretched by the falling weight, whose position is recorded on paper tape during the course of its descent. From the position versus time information, the work done on the sample is calculated. From this work input, in combination with the displacement data, the stress is obtained as a function of strain. The strain rate varies during the experiment. Different masses of the falling weight are used to map out the stress-strain curve. Note that the strain rate is not constant and the obtained modulus for any strain is the secant modulus (the average response of the sample over all strains up to the given strain), not the actual tangent modulus.
Villars, J. Appl. Phys. 21, 565 (1950), achieved strain rates as high as 2700 s−1 with a device employing a spinning wheel. A pin on the edge of the wheel grabs a rubber sample in the form of a loop, stretching it at an approximately constant rate. The speed of the spinning wheel is varied between 60 and 1700 rpm by a transmission and with speed-reducing pulleys. A piezoelectric crystal and oscilloscope is used to measure the force.
Gale and Mills, Plast. Rubber Process. Applic. 5, 101 (1985), achieved compressive strain rates approaching 200 s−1 with a falling weight apparatus. The 5 kg weight is dropped onto the sample, compressing it. Integration of accelerometers attached to the weight gives the energy required for compression of the rubber. The slowing of the falling weight is used to deduce the rebound (recovery) of the compressed sample. Thus, a measure of the energy input to and dissipated by the sample is obtained. Approximate force and displacement curves for foam test samples were obtained. The rate is not constant, the mode of deformation in not homogeneous, and the stress-strain data is only semi-quantitative.
Hoge and Wasley, J. Appl. Polym. Sci.: Appl. Polym. Symp. 12, 97 (1969), and Rinde and Hoge, J. Appl. Polym. Sci. 15, 1377 (1971), obtained high speed stress/strain measurements on a polystyrene foam by using the gas gun from a metal working machine (Dynapak Model 600). Release of the compressed gas expands a piston, which in turn compresses a foam sample at rates up to 100 s−1. A plate behind the sample limits the strain of the sample to 5% in compression. The force and displacement of the sample are measured with transducers. According to the authors the test method “does not provide valid modulus data”, particularly at low strains.
The instrument most commonly used to measure high speed mechanical behavior is the split Hopkinson bar, originally developed for steel but since applied to other materials, including polymers. See Yi et al., Polymer 47, 319 (2006). In the split Hopkinson bar device, a sample is placed between two long elastic bars, typically aluminum. A third, smaller “striker” bar is accelerated toward the incident bar. The reflected and transmitted pulses are measured, usually with strain gauges attached to the bars, and from these the properties of the sample are deduced. The requirement of dynamic stress uniformity limits the maximum deflection and minimum strain rate. See, Yang et al, Int. J. Impact Eng. 31, 129 (2005), Song et al., J. Eng. Mater. Technol. 125, 294 (2003), Rae et al., Polymer 46, 8128 (2005), Yi et al., Polymer 47, 319 (2006), Sarva et al, Polymer 48, 2208 (2007), and Amirkhizi et al., Philos Mag, 86, 5847 (2006)
The recent development of pulse shaping in the Hopkinson bar method provides nearly constant strain rates to moderate strains. See, Chen et al., Exp. Mech. 39, 81 (1999). For elastomers, spatially homogeneous uniaxial compression is difficult to achieve due to the tendency of these materials to adhere to the loading surface. This adhesion causes subtle “bulging,” indicative of mixed modes of deformation, for example, compression in the central region and shear at the interfaces. For thin cylinders this “barreling” necessitates a large correction of the measured data. See Gent et al., Proc. Inst. Mech. Eng. 173, 111, 1959; Mott et al., Rubber Chem. Technol. 68, 739 (1995); and Anderson, et al., Rubber Chem. Technol. 77, 293 (2004). Verification of truly flat cylindrical surfaces is complicated by the tradeoff between time and spatial resolution in the imaging of high speed measurements. See Song et al., J. Eng. Mater. Technol. 125, 294 (2003).
Hoo Fatt et al describe another high speed tensile test machine in Tire Sci. Technol. 30, 45 (2002); U.S. Patent application No. 20040040369; and Hoo Fatt et al., J. Mater. Sci. 39, 6885 (2004). In that device, the impact energy is supplied by a Charpy-type pendulum, which contacts a slider bar that pulls directly on cables attached to shuttles; sample grips are attached to the latter. FIG. 1 shows the slider bar and cables of this device. The speed of the slider bar is equal to the tangent velocity of the pendulum, so that the velocity of the cables is determined by the drop-height of the pendulum and the angle between the cables and the slider bar. The speed of the shuttles is therefore constrained to be less than the pendulum speed. Practical considerations, such as the available rigging space, will determine the lever length of the pendulum, which will apply constraints on the pendulum drop-height.
The pendulum tangent speed is equal to the slider bar speed, which is found by equation 1:v=(2gh)1/2 
where g is the acceleration due to gravity (9.81 m/s2) and h is the drop-height. Using the maximum drop-height of 1.52 m, as given, the maximum pendulum speed is 5.46 m/s. From FIG. 1, the cable speed is found from the component of the slider bar speed in the cable direction, as equation 2:vC=v cos α
where α is the angle between the cable and the slider bar. Since the displacement of the shuttles is equal and opposite, the total sample stretching velocity is twice that of the cable velocity. Given that cos α≦1, the maximum available sample stretching speed is 10.92 m/s. This maximum speed was incorrectly cited in the references as 16.93 m/s.
There is a need for a tensile impact instrument that provides uniform, homogeneous uniaxial deformation at an essentially fixed strain rate to high strains, with the entire experiment captured on video.